Which solution is correct? Be sure to check for extraneous solutions.
1 answer:
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Answer:
a) 2.5%
b) 97.5%
c) 16%
d) 84%
e) 50%
f) 50%
g) 84%
h) 16%
i) 97.5%
j) 2.5%
Step-by-step explanation:
The empirical rule, or the rule of 50%-34%-14%, states that:
In a normally distributed stat with mean and standard deviation
...
a) 2.5% of the scores are going to be above
b) 13.5% of the scores are going to be above and below
.
c) 34% of the scores are going to be above and below
d) 34% of the scores are going to be above and below
e) 13.5% of the scores are going to be above and below
f) 2.5% of the scores are going to be below
In this problem
We have that and
So:
(a) above 100, (b) below 100
So 2.5% of the scores are going to be above 100, and the other 97.5% is going to be below 100
c) above 90, (d) below 90
So 13.5% of the scores are going to be above 90 and below 100, and 2.5% of the scores are going to be above 100. So 13.5% + 2.5% = 16% of the scores are going to be above 90 and the other 84% is going to be below 90
(e) above 80, (f) below 80
80 is the mean, so approximately 50% percent of the scores are going to be above 80 and 50% are going to be below 70%.
(g) above 70, (h) below 70
34% of the scores are going to be above 70 and below 80, and other 50% percent of the scores are going to be above 80. So in all, 84% of the scores are going to be above 70. The other 16% of the scores are going to be below 70.
(i) above 60, and (j) below 60
So 2.5% of the scores are going to be below 60, and the other 97.5% is going to be above 100
Answer:
The length of the arc =
And the length of the full circle:
Step-by-step explanation:
To solve this problem we will be analyzing aright angle triangle that is formed when drawing the appropriate radius associated with the arc and the chord of a segment of circumference as depicted by the triangle shaded in yellow in the attached image.
Notice that the information given in this problem can be represented by:
1) the 90 cm width of the arc with the value of 2x (drawn in orange) in the drawing
2) the 30 cm of the arc's height with the value of y (drawn in green) in the drawing
In order to use the Pythagorean theorem in the little yellow triangle, notice that the hypotenuse is given by the radius R of the circle, and the two legs of the right angle triangle are given by "x" and "R-y"
So the Pythagoras theorem becomes:
Therefore, in our case, where x=45 cm, and y=30 cm, we have:
Now, with the radius, we can calculate the length of the arc of circle if we know the subtended angle in radians:
length of arc =
The angle subtended by the arc can be obtained by doubling the angle with vertex at the circle's center in our yellow right angle triangle. This is done via the sine function:
Therefore, length of the arc =
And the length of the full circle:
